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AC Measurements and DMMs

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Politecnico di Torino

M. Parvis

Digital Multimeters&

AC measurements

Politecnico di TorinoThis material freely available to Politecnico di Torino students forpreparation to the exam. Any other either commercial ornon-commercial use expressly prohibited without written consentof the author

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Time-varying quantities are usually characterized bymeans of few parameters

The first electricity use was to transfer energy andemployed DC supplies

Many equations used in DC can be used in AC if RMSvalues are used

The most important parameter (from this point of view!)is therefore the RMS value

AC voltmeters

!=T

dttv

0

2eff )(

T

1V

Measuring RMS values is not easy since it involves non-linear operations and circuits


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IFthe signal has a defined and known shape, the RMSvalue can be computed starting from other quantities.

Historically the signals were (only) sinusoidal thussomeone started to produce voltmeters that do not

measure the RMS value, but nonetheless do display it:

Voltmeters calibrated in RMS value, i.e. voltmeterscapable of displaying the RMS value IFthe signal is

sinusoidal

There are three basic types of AC voltmeters calibrated in

RMS

! (True) Root Mean Square (TRMS)! (rectified) average (AVG)! Peak

Voltmeters calibrated in RMS values

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Basic equations for sine signals

A peak voltmeter displays the RMS value if its output ismultiplied by 0.707

A (rectified) average voltmeter displays the RMS value ifits output is multiplied by 1.11

2V

eff

PV

= ! ==T

0

PPm

2Vdtt)sin(V

T

1V

"

#

m

m

effV11.1

22

VV !=

"


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Sine signal with peak value10V (RMS value 7.07V)

Type Measurement Multiplier Display

VRMS

7.07 7.07

VAVG

6.366 1.11 7.07

Vp

10 0.707 7.07

BEWARE it works only with sine signals!

Square signal with peak value10V (RMS value 10V)

Type Measurement Multiplier Display

VRMS 10 10

VAVG

10 1.11 11.1

Vp

10 0.707 7.07

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Each instrument actually measures (correctly) thequantity it is designed for

It is always possible to back-correct the output(decalibration) getting the (correct) original value

From average voltmeter it is possible to get the(real) average value by dividing by 1.11

From a peak voltmeter it is possible to get the(real) peak value by dividing by 0.707

NOTE: if the signal shape is known, from average/peakvalues it is easy to compute the RMS value

Decalibration


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(rectified) Average voltmeters

A rectifier + a DC voltmeter

Two possibilities based on the rectifier type:

Half-wave Full-wave

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Half-wave

Vi Vo

! ==

2/

0

)(1 T p

Pss

Vdttv

TV

"

ssssp

eff VVV

V 22.222

!==

"


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Full-wave

Graetz bridgeVi Vo

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Vi Vo

Full-wave


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Vi Vo

Full-wave

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T

0

p

Pds

V2dt)t(v

T

1V

mdsp

eff VVV

V 11.1222!==

"

VDC

ViV0


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Half-wave or full-wave?

Full-wave:

Reduced ripple i.e.more steady readings

Increased voltage dropon the diodes, thus

greater problems at

low amplitudes

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Example: the tester

The diode voltage dropturns out in a non-linearscale at low voltages

The manufacturer changesthe ticks to correct for thisnon-linearity


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Peak voltmeters

The capacitor charges to the peak value, and neverdischarges

A discharge resistor is added in parallel to thecapacitor

Vi

Vo

!A diode in series to a capacitor

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Vi VDC

RC>>T

A DCcomponenton the

signalalters theoutput

A galvaniccoupling isrequired for therectifier to work

!Two problems


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AC coupled peak voltmeter a.k.a zero

fix peak voltmeter

Vi Vo

VC

IC Vi

IC

VC

V0

The diode direction canbe reversed

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Vi VDC

The signal is shifted to have itsminimum value at zero

For a sine signal the shiftequals the peak value (withouttaking into account any DCcomponent)

A DC voltmeter is connected tothe output


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Advantages of the AC coupled peak

voltmeter

Does not require galvaniccoupling

DC components do not affectthe output

Can be easily arranged in theform of probe

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AC coupled Peak probe

2

1

21

2!

+ RR

R

Vi

Vm

Rs R

i

DMMProbe

IF Rs=0.4Ri , the DMM displaysthe RMS value (with sinesignals!)

With other signals thedecalibration must be used

BEWARE: if the signal is notsymmetric the output dependson the polarity


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(True) RMS voltmeters

Perform dttVT

V

T

eff !=2)]([

1

Useful for distorted signals and noise measurements.

Three basic types:

Electrothermal Digital Analogue

!Electrothermal Take advantage of the the thermal effect (V2/R)

connected to the signal

Usually by comparing thermal effects of theunknown AC signal with a DC aux signal

Slow, but extremely accurate

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Digital

An ADC is used to sample the singnal The RMS is computed by summation For good results:

Synchronous sampling and/or High sampling frequency

Good accuracy

!"

=

""=T

T

k

eff TkvTTV

1

2)]([



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Analogues

Employ non-liner circuits (usually log type) to perform: product v(t)v(t) average Square root

Available as integrated circuits Medium accuracy

Technology Uncertainty

Electrothermal 0.003%

Digital 0.01%

Analogue 0.05%

(DC) 0.0003%


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In brief

The different voltmeter types give the same resultsonly if the signal is of sine type

It is always- possible to decalibrateto getthe actual measured value

IF the signal shape is knownit is possible tocompute the RMS value

IF the signal shape is known it is possible topreview what every voltmeter should display

If the signal has DC components, the actualdisplayed value depends on the voltmeter coupling


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Inputfront-end

Based on Analog to Digital Converter

ADCProcessing

Display

Interface

Digital Multi Meters

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DMM resolution

Different ways of express the resolution

Maximum figure on the display NMAXDimensionless valueNumber of (equivalent) digitsusually computed as :

IF b=2 bits,

IF b=10 (fractional) number of digits

usually rounded according to the most

significant digit value:

0-1 0.5

0-3 0.75

0-9 1

MAXbNlog=!


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NMAX=9999 4 (4)

3.75

3.75

3.5

(3.6)

(3.5)

(3.3)

NMAX=3999

NMAX=3100

NMAX=1999

NMAX=1299 3.5 (3.1)

The net effect can be an abrupt resolutionchange

Examples

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ADC

Display CPU

Currentgenerator

Ampl. AC/DC

Swithc

Referencevoltage

In

Referencethe DMM cannot be better than itsreference

Usually a special zener of 1-10V Other internal standard can be present

Switch:to select different functions (V, I, R,..) Usually 2 to 5 inputs


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Switch and inputs

You may find

2 main inputs 2 sense inputs 1 current input A guard input

In simpler DMM the guard ismissing and often also the

sense inputs are missing

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Voltage

Only the main inputs are used

Atten.

Gen.IHI-S

HI

LO

LO-S

I Typical input

impedance 10M!


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The input impedance isrelated to the input

divider

On ranges up to 10 Vthe divider is not

required

Some DMMs allow thedivider to be

disconnected on these

ranges raising the input

impedance to >10 G!

Gen.IHI-S

HI

LO

LO-S

I

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Current

The measurement is performed byusing an internal shunt using the

auxiliary current input and the the

main input LO

Safer solution than inserting theshunt between the inputs

Gen.IHI-S

HI

LO

LO-S

I


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Resistance

An internal current generator isused and the voltage drop onthe unknown resistor measured

Current adjusted to havevoltage drops of few hundreds

of millivolts

The cable resistance affects theresults

Gen.IHI-S

HI

LO

LO-S

I

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4 Wire resistance

Employs main and senseinputs:

2 cables for current 2 cables for voltage

The cable resistance does notaffect the result


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Amplifier ADC with typical input range 10V The amplifier extends the input range to

10 - 100mV Noise and pass-band possible problems

ADC

Display CPU

Current

generator

Ampl. AC/DC

Swithc

Reference

voltage

In

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For AC voltage and current the AC/DC converter canbe

AVG TRMS

With coupling AC+DC AC only

ADC

Display CPU

Currentgenerator

Ampl. AC/DC

Swithc

Referencevoltage

In


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AC coupling

2

DC

2

DCeffACeffAC VVV

The AC coupling removes any DC component and

makes easier to arrange the circuits.

Two problems:

The measured RMS in the case of signals withDC component is

The AC coupling may add errors due to the highpass filtering action

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5ms/div 0.2V/div

Example: AC+DC

VVeff

4.0=

The RMS value does notdepend on ducy-cycle

VVdc

2.0)34.014.0(41 !="!"=

Example: AC

5ms/div 0.2V/div

The RMS value is connectedto the duty cycle

VVeffAC

35.02.04.0 22

!"=


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The crest factor

Signals with the same RMS value

eff

p

fV

Vk =Crest factor

The input analogue circuits must handle thesignals without distortion

From RMS it is not possible to compute the peakvalue

DMMs can handle only signals with limited crestfactor (e.g. 5-7)

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Two basic types on ADCs: SPOT Integrating ADC

ADC

Display CPU

Currentgenerator

Ampl. AC/DC

Swithc

Referencevoltage

In


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SPOT ADC The converted value is connected to a specific

signal value at a specific (very small) sampling

time

Integrating ADC The converted values is connected to the average

value in a certain (usually large) time interval

The aperture time (a.k.a. integration time) islarge by design

Used due to their properties: Low cost High accuracy (20-24bit) Reduce the differential mode noise at mains

frequency

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Frequency responseof the ADC forintegration time20ms

The integration acts as a low pass filter and reducethe noise: easy to obtain 20-24 bits

The integration nullifies components with periodequals to the integration time The integration time is expressed in PLC (periods of

mains)

50 100 150

0.2

0.4

0.6

0.8

1

Hz

A m p

i e z z

a


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Guard

connection

Some DMMs have a guardinput

Useful for noisereduction

Difficult to use The guard is connected to

the shield

It is not a groundconnection

HI

LO

G

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Example: measurement in the presenceof a common mode noise Vcm

The Vcm is attenuated by the differentialinput front-end

A connection LO - guard eliminated theVcm

Vd

Vcm


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Vd

If the cables have a not negligible impedance thecurrent which flows through the parasitic capacitance

may lead to errors The connection LO-guard makes thing worsen as it

increases the stray capacitances

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Vd

This connection removes the problem since the noisecurrent flows through the guard cable

In other cases a different approach has to be used


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Revision questions

Why the RMS value is often used for AC measurements? Why average and peak voltmeters are used, how are they

calibrated, what they measure?

What is the decalibration when and how can it be used? What does it means half-wave full-wave, how the circuits are

arranged, what are pros and cons of each circuit?

How a peak voltmeter is arranged? What are the differencesbetween AC and DC coupling, what are pros and cons of eachcircuit?

How a DMM is arranged, what does it means a resolution indigits?

How the front end is arranged, how may inputs can be found ona DMM, how are they connected during the use?

What is the typical input impedance, how can be increased issome cases, what is a 4 wires connection, where is it used andwhy?

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Revision questions

What does it means AC coupling for RMS measurements whatare the effects, why is it used?

What is the crest factor, how it affect the converted value? What does it means SPOT ADC /Integrating ADC what are pros

and cons of the two technologies?

What is the guard connection, how is it used?

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